The Feller property on Riemannian manifolds
The asymptotic behavior of the heat kernel of a Riemannian manifold gives rise to the classical concepts of parabolicity, stochastic completeness (or conservative property) and Feller property (or C 0 -diffusion property). Both parabolicity and stochastic completeness have been the subject of a syst...
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Published in | Journal of functional analysis Vol. 262; no. 5; pp. 2481 - 2515 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.03.2012
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Subjects | |
Online Access | Get full text |
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Summary: | The asymptotic behavior of the heat kernel of a Riemannian manifold gives rise to the classical concepts of parabolicity, stochastic completeness (or conservative property) and Feller property (or
C
0
-diffusion property). Both parabolicity and stochastic completeness have been the subject of a systematic study which led to discovering not only sharp geometric conditions for their validity but also an incredible rich family of tools, techniques and equivalent concepts ranging from maximum principles at infinity, function theoretic tests (Khasʼminskii criterion), comparison techniques etc. The present paper aims to move a number of steps forward in the development of a similar apparatus for the Feller property. |
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ISSN: | 0022-1236 1096-0783 |
DOI: | 10.1016/j.jfa.2011.12.001 |